following peculiar prescription: One must add up the waves for particle histories that are not in the ΓÇ£realΓÇ¥ time that you and I experience but take place in what is called imaginary time. Imaginary time may sound like science fiction but it is in fact a well-defined mathematical concept. If we take any ordinary (or ΓÇ£realΓÇ¥) number and multiply it by itself, the result is a positive number. (For example, 2 times 2 is 4, but so is -2 times -2.) There are, however, special numbers (called imaginary) that give negative numbers when multiplied by themselves. (The one called i, when multiplied by itself, gives -1, 2i multiplied by itself gives -4, and so on.) To avoid the technical difficulties with FeynmanΓÇÖs sum over histories, one must use imaginary time. That is to say, for the purposes of the calculation one must measure time using imaginary numbers, rather than real ones.
